Czech has only short [r=] and [l=], but, interestingly, can oppose
syllabic and non-syllabic [r] (some words with initial combination
<rv> have non-syllabic [r]). Syllabic [n=] and [m=] occur mainly in
loanwords (e.g. ending in [-Izm=]) and tend to acquire a short vowel
in the colloquial language (e. g. [-IzUm]).
Slovak has both short and long [r=] and [l=] (but, IIRC, no syllabic
parallel to its third liquid, the palatal<ized> [l']).
Serbian/Croatian has only [r=], which can be long and short and carry
all four accents, as well as occur in combinations like [pr=.o]
(disyllabic; perhaps in fact [pr=.ro]; historically, < monosyllabic
[pr=l]; I forget the exact translation, but the Russian parallel
sounds [p'or] and means '<he> was carrying with difficulty').

>What do
>they correspond to in Russian?

Oh, this requires a whole lecture in historical phonetics... If *very*
short:
PIE combinations like TR=(:)T- (T for any obstruent, R for '[r] or [l]')
became TIRT- (sometimes TURT- or TRIT-) in Proto-Slav (and Baltic; I and
U stand for i-breve and u-breve, the two short vowels later treated as
'reduced' in Slav).
All combinations of the types TURT-, TRUT-, TIRT-, TRIT- (of any origin)
become TR=T- in languages like Czech and Serbian/Croatian (but different
combinations at different time, at least in Czech; in Serbian/Croatian
[l=] later becomes [u]).
As TURT- and TIRT- violate the 'open syllable law', it is sometimes
argued that they were pronounced TR=T- already in Proto-Slav, and
actually haven't changed since the PIE times. A stage with TR=T- due
to the 'open syllable law' is probable for some languages (including
those preserving the syllabic resonants, like Czech, and those having
lost them, like Bulgarian), but (IMO) hardly for the East Slavic ones
(including Russian). No Slavic languages distinguish PIE TR=T- from
PIE TuRT- or TiRT-, but Russian does distinguish TIRT- from TURT-.
Russian treats I and U in TURT-, TRUT-, TIRT-, TRIT- the same way as
any other I and U that cannot become zero because of their position.
By the end of Old Russian period all such 'I's coincide with 'e', and
all 'U's with 'o'. They were subject to all the regular changes typical
of 'e' and 'o' (like [e] > [o] before "hard" consonants, quality
changes in atonic position, etc.). The etymological spellings with <e>
and <o> are preserved in most cases.
Accordingly, the Russian correspondences for Czech (etc.) syllabic
resonants are quite diverse... and the above accounts for only the
standard Russian development, not dialectal words.

>On a similar note, I once designed an alien language (Klln [kl<syl>:n] or
>some such name) that used syllabics much as other vowels, including
>[a]+[l<syl>] as a diphthong <...>

A natlang parallel is provided by Lithuanian. It has no syllabic
resonants, but combinations 'short vowel + [r], [l], [n] or [m]'
function like diphthongs (and are termed 'diphthongic combinations'):
they can carry two different accents, like ordinary diphthongs and
long vowels, and unlike combinations with obstruents.
It's really difficult to invent anything usable and having no natlang
analogies... ;)
Basilius